Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of (3+5*x)/(1+x)
-
Limit of (1-cos(6*x))/(x*sin(x))
-
Limit of 1/(-1+2*n)
-
Limit of x*cot(6*x)
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Identical expressions
- one /(- one + two *n)
- 1 divide by ( minus 1 plus 2 multiply by n)
- one divide by ( minus one plus two multiply by n)
- 1/(-1+2n)
- 1/-1+2n
- 1 divide by (-1+2*n)
-
Similar expressions
- 1/(-1-2*n)
- 1/(1+2*n)
Limit of the function 1/(-1+2*n)
The solution
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1 lim -------- n->oo-1 + 2*n
$$\lim_{n \to \infty} \frac{1}{2 n - 1}$$
Limit(1/(-1 + 2*n), n, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{n \to \infty} \frac{1}{2 n - 1}$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty} \frac{1}{2 n - 1}$$ =
$$\lim_{n \to \infty}\left(\frac{1}{n \left(2 - \frac{1}{n}\right)}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{1}{n \left(2 - \frac{1}{n}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u}{2 - u}\right)$$
=
$$\frac{0}{2 - 0} = 0$$
The final answer:
$$\lim_{n \to \infty} \frac{1}{2 n - 1} = 0$$
$$\lim_{n \to \infty} \frac{1}{2 n - 1}$$
Let's divide numerator and denominator by n:
$$\lim_{n \to \infty} \frac{1}{2 n - 1}$$ =
$$\lim_{n \to \infty}\left(\frac{1}{n \left(2 - \frac{1}{n}\right)}\right)$$
Do Replacement
$$u = \frac{1}{n}$$
then
$$\lim_{n \to \infty}\left(\frac{1}{n \left(2 - \frac{1}{n}\right)}\right) = \lim_{u \to 0^+}\left(\frac{u}{2 - u}\right)$$
=
$$\frac{0}{2 - 0} = 0$$
The final answer:
$$\lim_{n \to \infty} \frac{1}{2 n - 1} = 0$$
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty} \frac{1}{2 n - 1} = 0$$
$$\lim_{n \to 0^-} \frac{1}{2 n - 1} = -1$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{2 n - 1} = -1$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{2 n - 1} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{2 n - 1} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{2 n - 1} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \frac{1}{2 n - 1} = -1$$
More at n→0 from the left
$$\lim_{n \to 0^+} \frac{1}{2 n - 1} = -1$$
More at n→0 from the right
$$\lim_{n \to 1^-} \frac{1}{2 n - 1} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \frac{1}{2 n - 1} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \frac{1}{2 n - 1} = 0$$
More at n→-oo
The graph